x = [-6.860120914,
-4.324130045,
-4.358625055,
-4.358426747,
-6.955852379,
-6.661145254,
-6.355462942,
-6.118102026,
-7.115148017,
-6.815308569,
-6.519993057,
-6.204119983,
-5.853871964,
-6.109523091,
-5.79832982,
-5.482672118,
-5.171791386,
-4.851705903,
-4.517126416,
-4.143573228,
-3.709075441,
-3.499489089,
-6.300769497,
-5.953504836,
-5.642065153,
-5.031376979,
-4.680685696,
-4.329846955,
-3.928486195,
-8.56735134,
-8.363211311,
-8.107682739,
-7.823908741,
-7.522878745,
-7.218819279,
-6.920818754,
-6.628932138,
-6.323946875,
-5.991399828,
-8.781464495,
-8.663140179,
-8.473531488,
-8.247337057,
-7.971428747,
-7.676129393,
-7.352812702,
-7.072065318,
-6.774174009,
-6.478861916,
-6.159517513,
-6.835647144,
-6.53165267,
-6.224098421,
-5.910094889,
-5.598599459,
-5.290645224,
-4.974284616,
-4.64454848,
-4.290560426,
-3.885055584,
-3.408378962,
-3.13200249,
-8.726767166,
-8.66695597,
-8.511026475,
-8.165388579,
-7.886056648,
-7.588043762,
-7.283412422,
-6.995678626,
-6.691862621,
-6.392544977,
-6.067374056,
-6.684029655,
-6.378719832,
-6.065855188,
-5.752272167,
-5.132414673,
-4.811352704,
-4.098269308,
-3.66174277,
-3.2644011];

y = [ 0.8116,
0.9072,
0.9052,
0.9039,
0.8053,
0.8377,
0.8667,
0.8809,
0.7975,
0.8162,
0.8515,
0.8766,
0.8885,
0.8859,
0.8959,
0.8913,
0.8959,
0.8971,
0.9021,
0.909,
0.9139,
0.9199,
0.8692,
0.8872, 
0.89,
0.891,
0.8977,
0.9035,
0.9078,
0.7675,
0.7705,
0.7713,
0.7736,
0.7775,
0.7841,
0.7971,
0.8329,
0.8641,
0.8804,
0.7668,
0.7633,
0.7678,
0.7697, 
0.77,
0.7749,
0.7796,
0.7897,
0.8131,
0.8498,
0.8741,
0.8061,
0.846,
0.8751,
0.8856,
0.8919,
0.8934,
0.894,
0.8957,
0.9047,
0.9129,
0.9209,
0.9219,
0.7739,
0.7681,
0.7665,
0.7703,
0.7702,
0.7761,
0.7809,
0.7961,
0.8253,
0.8602,
0.8809,
0.8301,
0.8664,
0.8834,
0.8898,
0.8964,
0.8963,
0.9074,
0.9119,
0.9228 ];

X = [ x.^0, x.^1, x.^2, x.^3, x.^4, x.^5, x.^6, x.^7, x.^8, x.^9, x.^10];

# solve y = X c for c

c = X \ y

cov_direct = inv(X' * X);

[Q,R] = qr(X);
cov_qr = inv(R'*R);

cov_direct/cov_qr